Instrument for drawing conic sections



Dec. 1, 1953 M. POLAKOWSKI 2,660,790

INSTRUMENT FOR DRAWING CONIC SECTIONS Filed July 30, 1951 2 Sheets-Sheet 1 INVENTOR.

INSTRUMENT FOR DRAWING CONIC SECTIONS Filed July 30, 1951 Y 2 Sheets-Sheet 2 A IN VEN TOR. Warm Pam/[0405a,

Patented Dec. 1, 1953 INSTRUMENT FOR DRAWING *CONIC .cSECTIONS Marianlolakowski, Qhieago, 111. Application- 11115 430, 1951, Serial=.No.,239,215

(Cl.33- -j27) ZQQIai n s.

l ,Th present n enti re e man anese for drawing conic sections, includingellipsehy- ,;pe1;bol a and parabola.

The principal object of thepresent invention .is -;the provision of a point.oarrying arni and-a scribing arm, the latter ,angularly adjustable with relation to theformen'and the two set ,within a s upport for a rotary shitting movement, with the Y pencil in the scrib'ing; arm supported in thearin lander a tension tending to urgev said peneil outwardly of said scribing arm, so that when the two arms are set at -an angle with r-elatien to the ,paper on which an ellipse .is to be drawn, and irigidly supported in anangular-relation with re- ,l 'i t the paper, a el rseg dese 'ibed .by the scribing arm when the two arms are EQW' F-l- Another object of the present; invention is the provision in the instrument of the eharacter noted of ajpoin t carrying -armeorres ponding to the axis of a cone withalongitudinally yieldable ,js cribing arm in an :angular relation with the point earryingarm, said soribing arm positioned upon a line corresponding tothefgenerator of eone, with the two arms rotatablysnpported by jasuitable support, whereby an ellipse rnay be described by a cr bin m. hmbothz rm isr positioned upon an angle relativeto ,the paper upon which an ellipse is ;to be .-des crihed, and t e er m emen i -imrar sdt th -tw "arms so that thescribing arm mayJnoveepicy- .clically with relationto the pointcarrying arm,

the lattenrotating upona fixed point on a paper sheet.

Astill further object of the present invention .is the provision of an instrument.capable of du- 'plicating an ellipse of given transverseand con- 'j.ugate axes, which objectmay be accomplished by a slight modification of the instrumenthereinabove indicated, and which -modif ication con- ..sists of a provision of an additional point supporting arm upon a common plane with, the other 'two arms, said additional point oarrying .arm being disposed at a point opposite from thatof T the scribing arm and upon a line of the opposite generator of a cone.

Another object of the present invention is the provision of a suitable support whereby the point carrying arm correspondi'ng to the axis of a some may be maintained in a parallel relation with the paper and whereby, by means of the scribi ll aa a rbo m b 14.9 1 3 paper sheet, when the two arms are rotatably l sh i dw th pencil po pa it th se Yin armine sa emem t t aper s eet.

A still further object of the present invention is -the provision of a suitable support whereby tihe .point carrying arm corresponding to the 0 her generator of a cone may be supported. ina p a1- -le1 relation with a paper sheet, so that whenall -ofit he'arrns are rotatablyshifted, with thescribing arm in contact with the paper, a paranoia rgay be I described upon the paper sheet.

With t abfive en a isc i t erge others that will appear as the invention isp understood, the same .consistsin; the :novel v structiom combination and. arrangement of a1;ts hereinafter more fully described, illustrated in the accompanying drawings and pointed out th a p nd claim .l th drawings orm n a rro asm nation and in which like designatingcharabters refer to eorrespon eral views:

n pa hr g o -tease ..Fig. 1 represents an ellipse having, deter r inaple transverse and conjugate axes to be duplicated by its eiio ft r n m t Fig. 2is. aside elevational view of the present instrumentin "its one of the initial positions preparatory to the step oi describing Fig. 3 is a top elevational viewof the present instrumentwhen in a position shown i n'Fig fzi' Rig. 4 is a sideelevational view ofithe ins tru- 'ment of a slightly modified construction, while'in a position in which the same is'eapable] of drawing..a hyperb ola;

Fig. 5 is a similar View ofthe instrumentiofl a ,modified construction illustrating its position preparatory to the drawing of a parabola there- "Fig.5 is an enlargedelevational view ofa part of the instrument, partly in section, I taken, along linea -5 of Fig.4; 40

.Fig. 7 is'an enlarged longitudinal cross sectionalview through one of thearms constituting a part {if the instrument; and

Fig. 8 is an enlarged planelevational view' of a cross arm constituting a part of the presentinventiori taken on line s- 8 of Fig. 2.

Referring in detail to the present drawings,

and moreparticularly to the formf ofthe' in infrn'ent designed to draw or duplicate an" se,

shown in Figs.) and 3, the same includes tubular member H), which constitutes apart bf th'central point carrying arm. The uppersolidfe nd of said tubular member {0 which is Sam what redueed in diameter is passed'through bross sun 1 I and centrally thereof, and there'the same-is iri'cti onally held. Inapivotal association each end of said cross arm I l is a similar tubular member 12, the upper end of which terminates in a solid fiat piece l3 which enters slot l4 made at the end of cross arm ll. Set screws I! passing through the ends of said cross arm ll, opposite slots I4, engage and bear against fiat ends I 3, for maintaining said members 12 in an angular adjusted relation with member 16.

In a telescopic relation with each of said arms H) and I2 is a cylindrical rod 46, the outer free end of which is sharpened to define point H. In case of one of side rods l6, pencil-supporting member I8 is afixed to the lower end thereof by means of set screw 19, for supporting pencil lead 20.

Interposed between the inner, upper ends of said rods 15 and the upper, solid end portions of said cylindrical members In or l2, as the case may be, are coil springs 2i, normally urging said rods 16 to shift outwardly of said cylindrical members l2. The lower end of each of said members In and I2 is provided either with an integrally formed or frictionally engaged ferrule 22, through which set screw 23 is passed for maintaining rod H3 in an adjusted extended position with relation to each of said tubular members I or l2, as the case may be.

The upper, reduced, solid end of said tubular member is passed through eye 24, formed at one end of arm 25, whereby said upper, reduced, solid end of said tubular member I0 is frictionally and rotatably supported within said arm 25. The outer termination of said upper end of tubular member If! is knurled for facilitating manual rotation thereof within said arm 25. In

a pivotal connection, through set screw 26, with the opposite end of said arm 25, is link 27, which at the opposite end is provided with an enlarged head 28, which extends laterally of said link 21, as is seen in Fig. 3. generally indicated by 29 are in a pivotal connection with said head 28. Each of said legs 29 includes tubular member 30, sharp-pointed cylindrical rod 3|, telescopically received within said tubular member 30 and under tension by a coil spring identical to that of coil spring 2|, which spring is enclosed within said tubular member 30. Set screw 32 passing through the lower end of said cylindrical rod 3! maintains the latter in its extended adjusted position.

The upper ends of said tubular member 30 are solid and flattened, each flat end thereof being in contact with the end of said head 28, and being clamped thereto by set screw 33. By virtue of this arrangement legs 29 may be angular-1y shifted with relation to link 21 and clamped by set screws 33 in their angular adjusted position. It is noted that each of said legs 29 is identical in its construction with the construction of the arm which includes tubular member 12 and rod 16.

If it be assumed that the point carrying arm, including tubular member I!) and its cooperating rod I6 corresponds to the axis of any given cone, and if it be further assumed that the two angles enclosed by each tubular member I2 and tubular member l0 are equal, then the two arms which include said tubular members l2 are coincidental with the generators of a given cone, whose apex A would fall at a point of the intersection between the imaginary extension lines of said tubular members [2 and on a line of said reduced upper end of tubular member l0. As is seen in Fig. 2, if the central rod I6 is extended to point 0 and the pencil carrying rod I6 is extended to point C. with the remaining rod [6 being in con- A pair of supporting legs,

1 erator lines of a given cone.

tact with point B, and assuming that tubular member Hi with its rod 16 being in a perpendicular relation with line BC, in that event were the central arm with the side arms simultaneously rotated by turning at the knurled end of reduced upper end of said tubular member 10, the assembly would constitute a compass capable of describing a circle BDCE, which would correspond to a conic base of a projected cone of which the central point carrying arm, including tubular member It and its rod 16 would constitute an axis, and the side tubular members l2 and their cooperating rods it would coincide with the gen- For this reason in the following description the central point carrying arm, including tubular member ID and its cooperating rod 16 will be referred to as an axial arm, one side arm, including tubular member l2 and its cooperating rod it which carries pencil attachment l820 will be referred to as scribing arm, and the opposite side arm will be referred to as the generating arm.

Referring now to Fig. 1, there is shown an ellipse BHFG, having the transverse axis BF and the conjugate axis GH, with center 0, at a point where the two axes cross and bisect each other. The length of each axis may be known or unknown. To duplicate the ellipse of Fig. l and to draw the same upon a sheet of paper, the first step resorted to is the drawing of a straight line BX on sheet 34. The next step is to place the sharp point of the axial arm upon the center point 0' of the ellipse of Fig. 1, taking care that said axial arm be maintained in a perpendicular relation upon the sheet on which said ellipse of Fig. 1 has been drawn. While preserving the perpendicular position of said axial arm with relation to the paper on which said ellipse of Fig. l is found, the pencil point of the scribing arm is then placed at one of the end points G or H of the conjugate axis GH, while the sharp point of the opposite generating arm of the instrument is placed at the opposite end point of said conjugate axis. When the sharp point of the axial arm has been placed at point 0" of the ellipse, with rod iii of said axial arm fully extended, then screw 23 of said axial arm is tightened so that rod 16 may be rigid with tubular member Hl. While maintaining said axial arm in a perpendicular relation with the paper upon which ellipse of Fig. 1 has been drawn the remaining generating arms, with their rods I6 freely movable are manipulated until the point of one rod [6 and the pencil point of the two generating arms come in contact with the end points of the conjugate axis of the ellipse. While this manipulation goes on, care of course must be taken that the angles enclosed by the generating arms and the axial arm are equal. The operation of screws IE will assist in arriving at that result. When said angles are equal, with axial arm in a perpendicular relation with the paper, and with the sharp points of the generating arms in contact with the end points of the conjugate axis, and with the sharp point of the axial arm resting upon point 0', the set screws 23 of the generating arms as well as set screws I5 are tightened. When this is done the generating arms with the conjugate axis of the ellipse describe an isosceles triangle, with said conjugate axis forming a base thereof, the generating arms the sides thereof, and the axial arm an altitude. It is further noted that when the instrument is removed from the ellipse of Fig. 1 with its arms and rods l6 rigidly locked by manipulating screws i and" 23, the distance"l netween the sharp point'of rod l 60f one-generating arm to the pencil point of :the scribing arm will be equal to the length o'f'the'c'onjugate axis =GI-l3 of the ellipse of Fig; l. It must also necessarily follow that the distances between the sharp point of the axial arm and the' sharp'point-ofeither of the generating arms are equ-al. It isfurther noted that all of the arms extended by the last hereinabove described operation had for its purpose the determining-the axis and the" generators of acone of which ellipse of Fig. 1 was a section. The same can be readily visualized by reference to Fig. 2 wherein the dotted lines together with the arms ofthe instrument represent the axis and the generatorsandthe base of a projected cone ABC or w l'iidhthe ellipseof Fig. -1 is a section.

01'' course the imaginary projection of a cone indicated by the dotted lines shown in Fig. 2

wouldnecessarily be below paper sheet 36, be-

cause said paper sheet, being the medium upon which to receive the duplication of the ellipse of Fig. 1;,11'I1US13 necessarily represent the-plane of the elliptical section .of the said imaginary cone.

The next step in the method of duplicating a given ellipse is the markingoff of the length of the transverse axis of the ellipse of Fig. 1 upon line BX, by marking point F upon said line, so that-point- B thereon and point P thereon will mar-lithe ends Band F, respectively, of the transverse" axis 'of the ellipse of Fig. 1.

The next step in the method of duplicating a given ellipse by the present instrument is the positioning of the points of the three arms of the instrument upon line BX, with the point of the generating arm resting upon point B oi the line, with-other two'arms distanced from it along said line BX. Thereupon set screws 23 upon the axial and scribing arms are loosened and the instrument is then tilted, without however disturbing L the contactual relation of the sharp point upon the genera-ting arm with point B. Due to the tilting of the instrument and by virtue of the loosened set screws 23 upon said axial and scrib- "i-ng arms, rods It thereof will be forced to shift within tubular members ill and I2,- respectively, compressing their respective coil springs'zl', and the tilting is continued until the pencil point of thescribing arm reaches point F and comes to rest thereon. When that has been brought about set screws 23 upon the axial and scribing arms are then tightened, and supporting legs 29, which 'thereto'fore have been in an elevated inoperative position, are brought down until the sharp pointsof rods 3! have come in contact with paper sheet 34. Just 'where the sharp points of rods 3! Will engage and contact with said paper sheet is not important, the distance thereof from "the three arms of the instrument may be varied and may be entirely optional. What is important is that said legs 29 should support the in- 'strument in'its ultimate position last hereinabove described, and during the entire time of manipulation of the arms, until the scribing of the ellipse is completed. Of course, set screws 26, '33 and 32 should betightened in order. to firmly and rigidly support the three arms of the instrument in its ultimate position last hereinabove described.

Preferably the sharp points of rods 3 each should'engage paper sheet 34 at an equal distance from said line BX, because such position of legs 29,, with relation to paper sheet 34 will more readily assure vertical and perpendicular position of said three arms of the instrument with relation to sheet 34, which position is required in order to bring an accurate duplication of an ellipse;

From what has been said it is readily apparent that that ultimate position of the three arms places the three arms upon the-conic lines of an imaginary cone of which an ellipse to be -du-' plicatedzis a section, as is clearl-yse'en from' Fig. 2.

The next step in the operation is to loosen set screw 23 in the generating arm and shifting rod :6 completely into its tubular member 12, :and as tar as the same will go, and then tightening said set screw :23 in .order to maintain said rod [.6 fully within its tubular member 12-, for preventing interference of said generating arm during the scribing operation.

Next, set screw :23 upon the scribing arm is loosened.

While maintaining the relative mutual position -of.axial andscribingarmszand their relation with the paper sheet 34, the final operation is resorted to. That operation includes firmly grasping arm 25:01" link 2.! .by the fingers, and then imparting rotary movement to the axial arm by manually r rotating the latter .by turning the knurled free end of said axial arm, which extends above said crossarm H.

The rotary motion imparted to said axial arm should not of course disturb the relative mutual positions'thereof and of legs 29 or their relation to paper sheet .34. The rotary motion imparted to said axial arm will of course impart an epicyclic motion to the scribingarm and to the pencil point carried thereby, andcoil-spring 2i continuously exerting pressure upon rod I28 and the pencil point of said scribingarm will maintain the pencil point incontact with the paper during the said epicyclic motion of said scribing arm until the describing 50f the ellipse has beencompletecl.

The one-half of the revolution upon axial .arm will of course .bringythe scribi-ngarm and its pencil point to point But line BX, that is to the position formerly occupied by the generating arm now inoperative. This is one of the proofs that the pencil point of thescribing arm must necessarily be upon LthE elliptical-orbit. The definite proof of this resides in the fact that .the shifting 'of the scribing arm is along the plane .of the side ofthe imaginary projected cone, as is seen in Fig. -2,and since paper sheet v34 constitutes .a.section plane through a given cone, it therefore necessarily must follow that the pencil point upon the scribing arm describes an ellipse, and none other but the ellipse of Fig. '1, because the enclosed angle between the axial arm and the scribing arm remains unchanged from :the time that the conjugate axis of the ellipse of Fig. 1 was initially measured.

As is obvious, the generating arm of the instrument may be entirely eliminated and only the axial and the scribing arms used. In that instance it is possible todescribe any ellipse with no predetermined measurements however. 'By

such an instrument, devoid of the generating arm, no ellipse of known conjugate and transverse axes can be described. However, such partly stripped instrument may find great many uses where an accurate drawing of an ellipse is required without the predetermined lengths of its conjugate and transverse axes.

Referring now more particularly to the modified construction of the instrument capable of describing hyperbola and parabola the main parts of the-instrument, including *theaxialarm and the two generating arms, one of them being a scribing arm, remain unchanged. Thus, the axial arm includes tubular member ID, and the generating arms include tubular members I2. Rods l6 slidable within said tubular members [I] and 12 are actuable by coil spring 21 as shown in Fig. '7. Cross arm ll through which the reduced end of tubular member ID extends is capable of rotary movement with said arm i 1. Other two arms are pivoted by their reduced flattened ends l3 within the ends of said cross arm H, and are rigidly held in their adjusted positions by means of screws I5. Pencil attachment is carried by the outer end of rod 19 coacting with one of said tubular members l2.

The modification for the instrument capable of describing hyperbola and parabola consists only in the supporting means for the instrument. The said modification includes collar 36 within which the reduced end It of tubular member in is receivable. Collar 36 with said reduced end It is positioned within block 31, which in turn is positioned within arms 38 of the bifurcated end of cylindrical bar 39. The opposite end of said bar 39 terminates in a bifurcated head 40 within which the reduced end of extension 4| is receivable. The opposite end of said extension 4| is telescopically received within tube 42, where it is clamped by set screw 43 in order that said extension 4| may be held in its adjusted position. The reduced end of said extension 4| receivable within head 40 is clamped therein by means of set screw 44. Said extension 4| may be replaced by a longer or shorter extension depending upon the desired distance of the scribing arm or other arms from the paper upon which hyperbolic or parabolic sections, as the case may be, are to be described. One or two legs 45 are pivotally connected to the opposite end of tube 42, and thereto clamped by means of set screw 46 in order to hold said legs 45 in their rigid adjusted relation with said tube 42.

Ferrule 41, made at one end of protractor plate 48, encompasses bar 39 for the purpose of permitting shifting of said protractor plate 48 to or away from the axial and generating arms of the instrument, as is indicated in full and dotted lines in Figs. 4 and 5.

Said protractor plate 48 is provided with a scale of degrees to indicate parallel position of the axial arm and of the generating arm (other than the scribing arm) with relation to paper sheet 49, while drawing a hyperbola and a parabola, respectively.

Referring more particularly to Fig. 4, and bearing in mind that a hyperbola is a curve usually formed in a right circular cone by a section which is parallel to the axis of the cone, then it will be readily seen that when the axial arm of the instrument is in a parallel relation with paper sheet 49, as seen in Fig. 4, then the curve which will be described upon paper sheet 49 must be a hyperbola when the arms of the instrument are rotated to the distance of approximately one-half of revolution of the axial arm. The revolving of the arms is only as long as the pencil point in the scribing arm of the instrument shifts upon the paper sheet. The resulting line made upon the paper must be a curve, because as said scribing arm makes a shifting motion rod IS with its pencil attachment 35 shifts into one or the opposite direction, under the actuation of coil spring 2|, when set screw 23 is maintained open. Of course, during the rotatable shifting movement of the arms, legs 45 should be pressed firm to the paper sheet so that the instrument would not shift during the process of scribing a hyperbola upon the paper sheet. Also, the supporting arm, including bar 39, extension 4l, and tube 42 should be on a perpendicular plane with relation to the paper sheet, while the arms of the instrument are rotated. 7

Referring now more particularly to Fig. 5, and bearing in mind that parabola is the intersection of a cone with a plane parallel to its side, when the generating arm, which corresponds to the side of a cone, is in a parallel relation with paper sheet 49 the latter representing the parallel plane upon which a parabola is to be drawn, then when rotary movement to the arms is imparted, the scribing arm of the instrument must necessarily describe a parabola upon paper sheet 49, provided that set screw 23 of the scribing arm is loosened so that rod l6 and its pencil at tachment 35 may be actuable by coil spring 2| during the impartation of a rotary movement to the arms.

It is further noted that collar 36 is engaged by set screw 50 passing through one arm 38 of the bifurcated end of bar 39, for maintaining said collar rigid in its adjusted relation with arms 38. When said set screw 50 is loosened block 31 may be angularly shifted in order to adjust the arms of the instrument with relation to paper sheet 49, as may be indicated by protractor plate 48 so as to bring the axial arm in parallelism with the paper sheet or to bring the generating arm in parallelism with the paper sheet, preparatory for describing a hyperbola or a parabola, respectively. When the angles have been determined, then set screw 59 is tightened to rigidly lock collar 39 and block 31 to arms 38 and bar 39, and thereby also the reduced end l9 and through it the entire drafting instrument.

It is also noted that protractor plate 48 being swingable upon ferrule 41, when the proper angles of the axial arm and of the generating arm have been found and determined, and the drafting instrument has been locked to the supporting part of the device by means of screw 59, then said protractor plate 48 is swung to its inoperative position, indicated by dotted lines in Figs. 4 and 5, in order that the same may notinterfere with the rotary shifting movement of the arms.

Said rotary shifting movement may be imparted to the three arms either by turning the free end 10 which may extend beyond collar 36, or, if preferable, said reduced end 10' may be provided with a knurled knob 51 whereby the arms of the drafting instrument may be rotated.

As was hereinabove noted the supporting arm, including bar 39, extension 41 and tube 42 must be in a perpendicular plane with relation to paper sheet 49. However, it need not be in a perpendicular relation with the paper sheet. This is indicated in Fig. 5 where said supporting arm is slanting in one direction, although it still would be in a plane perpendicular to the paper sheet, just as the arm of Fig. 4 is.

Just as in case of an ellipse the paper sheet or any other medium upon which an ellipse was to be drawn represented a conic section plane and was in effect a bar preventing the arms of the instrument to shift by their free ends to the base of the imaginary projected cone, and by virtue thereof the paper sheet was capable of receiving the elliptical curve made by the point of the scribing arms, so also in the case of drawing hyperbola and parabola the paper sheet or other medium constitutes a conic plane barring the pencil point to pass beyond it, thereby forcing it to shift upon hyperbolic and parabolic curves, respectively. Since in the instance of a hyperbola the medium is in parallelism with the axis of an imaginary cone, and in case of a parabola, the same remain in a parallelism with a generator of an imaginary cone, and since in each instance the medium remains within the confines of an imaginary cone, it therefore must follow that the pencil point of the scribing arm must shift upon hyperbolic and parabolic curves, respectively, on the face of the medium with which the pencil point is in contact.

For all practical purposes while drawing a hyperbola one generating arm other than the scribing arm may be Wholly disregarded or eliminated from the instrument. This hold true with the axial arm while drawing a parabola.

While there are described herein preferred embodiments of the present invention, it is nevertheless to be understood that minor changes may be made therein without departing from the spirit and scope of the invention as claimed.

What I claim as new is:

1. A drafting instrument for drawing conic sections comprising a pair of generating arms, an axial arm disposed between said generating arms, said generating arms and said axial arm being upon the same plane, tensioned rod telescopically carried by said arms, a scribing fixture carried by the rod upon one of said generating arms, a cross bar, the ends of said generating arms being pivoted to said cross bar, the end of said axial arm being rigidly connected with said cross bar at a point median of the points at which the ends of said generating arms are pivoted, the enclosed angles between said generating arms and said axial arm being capable of adjustment by shifting said generating arms upon their pivots to or away from said axial arm, means for locking said generating arms in their angular adjusted position with relation to said axial arm, said axial arm and said generating arms being capable of angular shifting with relation to the medium upon which a conic section is to be drawn, means for supporting the arms in their angularly shifted position relative to the said medium, means for imparting a rotary shifting movement to the generating arm carrying said scribing fixture along a surface corresponding to the side of a cone, and tensioning means for actuating said scribing fixture along a curve which corresponds to the section of a given cone.

2. An instrument for duplicating an ellipse comprising a pair of generating arms, a cross arm at which an end of each of said arms is adjustably pivoted, an axial arm in a rigid relation with said cross arm at a point median of the points at which the ends of said generating arms are engaged, telescopically receivable rods coacting with all of said arms, a scribing fixture carried by the rod coacting with one of said generating arms, tensioning means in said arms normally urging said rods to shift outwardly, means associated with each of said arms for rendering said tensioning means inoperative in any selected arm, the outer end of the rod in one of said generating arms other than the one carrying said scribing fixture and the outer end of the rod associated with said axial arm each being provided with sharp point for selectively or simultaneously engaging the medium upon which a given ellipse is to be duplicated, said arms being capable of angular shifting with relation to the medium upon which a given ellipse is to be duplicated, the angular shifting of said arms being against the action of said tensioning means in at least said axial arm and the generating arm carrying said scribing fixture for depressing the rods thereof against said tensioning means, means for rigidly supporting said arms in their angular position with relation to the medium upon which a given ellipse is to be duplicated, and means for imparting a rotary movement to said axial arm, said last named means being operable when the generating arm other than the one carrying said scribing fixture is lifted from its engagement with the medium upon which a given ellipse is to be duplicated, on operation of said last named means the generating arm carrying said scribing fixture being adapted to shift upon the surface corresponding to the side of the cone of which the given ellipse is a section, the shifting of said latter arm inducing said scribing fixture to trace the duplication of the given ellipse upon the medium.

MARIAN POLAKOWSKI.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 623,227 Veronese et al. Apr. 18, 1899 1,139,298 Keppy May 11, 1915 1,286,770 Rashkovsky Dec. 3, 1918 1,456,970 Caldwell May 29, 1923 2,551,747 Ille May 8, 1951 FOREIGN PATENTS Number Country Date 854,680 France Jan. 24, 1940 

